I’m having a hard time wrapping my mind around some principles of Relativity and I need an assist.
If a ship was traveling very near the SOL and I could somehow make all matter (stars, planets, etc.) disappear, would the ship still be traveling at the SOL?
If a ship was traveling at the SOL and it shot a light beam out in front of it, would the beam still be traveling at the SOL or twice, which is impossible. Right?
Yes.
Light is a constant, it always travels at the same speed, regardless of the speed of the source.
The answer to your first question becomes much more obvious when you state it with the necessary explicitness. Speed only has meaning as a measure of how two bodies are moving relative to each other, so you have to specify the speed of your ship relative to something. If your ship is traveling at 0.99c relative to the sun, and then you make the sun vanish completely (along with everything else), how fast is the ship traveling relative to the sun? It isn’t: the sun doesn’t exist anymore, so speed relative to it no longer has any meaning.
To properly phrase your second question, you should also be specific about frames of reference: when you ask “would the beam still be traveling at the SOL?”, relative to what are you asking? Of course, with light it turns out that it doesn’t matter which frame you’re asking about: the tricky thing about light is that it travels at the same speed in all frames of reference. That is, no matter what you measure its speed relative to – the spaceship emitting the beam, a different spaceship traveling in the opposite direction, an observer on a nearby planet – the answer is always the same. A big part of relativity is figuring out how this is not actually a blatant contradiction as our naive intuition would suggest.
Another way to look at question 1 is that, even when you’re traveling “close to” the speed of light, you’re still not close to it, and in fact are perfectly at rest… in your own reference frame. No matter what you do, you’re always just as far away from the speed of light.
Two supplentary quetsions:
According to the OP, only matter disappeared. Photons still remain. So it’s still just as easy to measure position relative to where the sun was as it ever was, right? In theory you could measure your velocity relative to a star a light year`away using the same method that you always used, since you have a year’s worth of photons coming your way.
Even if the photons also vanish, imagine our ship is accelerating, approaching C with the engines at full power. Then we turn off all the matter. According to you the ship is now stationary. So where is all that energy from the engines going?
You seem to be saying that the ship can never move again in this universe, and yet just a millisecond before the engines were generating so much power they could accelarate a mass from .90C to .95C. Nothing’s changed, Fuel is still being burned at the same rate, but now you are saying it’s impossible for work to take the form of motion. So where is that energy going to?
This relativity thing produces some weird results.
The situation given was not that the ship was accelerating but rather traveling at a constant velocity relative to some inertial frame. If you remove all matter then the ship isn’t stationary; velocity simply becomes kind of a non-issue since velocity must be measured relative to some frame. It’s not that anything about the ship has changed, it’s that you can no longer meaningfully describe its velocity. You can’t tell you’re moving.
If you add acceleration to the mix then you are no longer in an inertial frame, you continue to accelerate as long as you have fuel to burn. You still can’t measure your velocity but you can certainly measure your acceleration as a force felt inside the ship.
Good point, and I’m not up on this stuff but I believe if you can still see photons from an object that’s no longer there, you are also subject to gravitons, so if the sun disappeared we would still feel its gravity from Earth for, what, 8 minutes? So hurtling through matter-less space in your ship you would still be subject to the gravity of anything you could still see.
Actually, as soon as you fire the engines, you once again have something to measure against: the reaction mass spewing out the back of the engine. Your velocity can be measured relative to that. But as to acceleration, CookingWithGas is right.
But what if your ship doesn’t have a reaction mass? What if it’s spewing forth light? You can’t measure anything meaningful from the relative velocity: by definition it’s travelling away from you at the speed of light. And yet, you’re still being accelerated: still moving relative to something, right?
Even with no other mass in the universe, and as long as you set a zero point, (say the moment when all matter disappeared,) you can measure the acceleration and duration of acceleration from that point on and calculate your velocity relative to the starting point. (i.e. where the ship would be if no accelerations took place.)
OK, that makes sense.
But couldn’t we then use the energy needed for acceleration/decelaration to deduce speed?
What I’m thinking is that we have a ship of known mass. And we know the efficiency of the engines. So, for example, it will take 2 units of fuel to accelerate the ship from .1C to .2C in an hour, and 4 units to accelerate it from .2C to .3C in the same time, 8 units for .3C to .4C and so forth. And I know I burn 2.6 units of fuel in an hour. And I measure the acceleration force as being equivalent to .1C. From that, can’t I then calculate that my current velocity is .22C?
It seems that since velocity is dependent on the energy used (less any inefficiencies), if we know how much energy is used we can use that to calculate a meaningful velocity regardless of any external reference frame.
And to pre-empt someone saying that we can’t know our starting velocity, we can by using the same method as given above. By directing the engines in different directions we can measure how much energy it takes to move in each direction. If the ship is travelling “north” at .1 C then we’ll use 2 units of fuel to accelerate .1 C. If it’s travelling at .2C then we’ll need 4 units to achive the same acceleration.
Obviously you couldn’t calibrate the engine’s efficiency in a matterless universe, but can;t we calibrate them before the matter vanishes and then use that same calibration afterwards?
Like most of these sorts of questions, your question is at once simple and deep.
Within current paradigms of what the universe Really Is, your question can be dealt with only using the descriptions which result from the theories of Relativity. Unfortunately, the theory of relativity encompasses a paradigm that helps describe matter, energy and time but it does not describe the most perplexing question of all: What is the fabric of space itself? What is left if we remove “everything” that is not space (matter, energy…everything). I realize you did not specify that when you asked your question, but I think that is what you are getting at–i.e. is something moving if there is nothing relative to which it is moving.
This is not a new question (they seldom are) and in my opinion cannot be answered in any current modeling of how the universe works. We conceptualize space as if it were…well, space…and as if everything sort of lived “in” space. We also, under current models, don’t think of space itself as some sort of aether through which things move–there have been some neat ways to “prove” that, at least as the aether was traditionally thought to be. At the same time, space is not nothing. The universe is expanding, but it is not expanding “into” space. Space itself is expanding under current models, but it is not necessarily expanding into any bounded limit the way that an expanding balloon might be described, for instance.
So what happens when you remove everything that is not space itself (except for, in the case of your example, one thing). Can that thing be said to be moving at all if the only frame of reference is tied to whatever “space” is? And what about the whole speed of light/relativity thing? In current modeling, velocity and acceleration always take place within a frame of reference, so it’s easy to conceptualize light zipping away from your ship at the SOL. And it’s actually fairly easy, if counter-intuitive, to grasp an understanding of how current modeling describes the SOL from the reference of a given spacetime frame so that the SOL is always constant in the medium in which it’s traveling (space, in the case of your OP).
But…until we can figger out what “space” is, we will not be able to understand the more fundamental answer to your question. I have my own notions about the Theory of Everything but will not bore you with the equivalent of a homeopath weighing in on treating cancer.
I might suggest beginning with one of the better layman’s books on the topic: The Fabric of the Cosmos, by Brian Greene. You won’t find answers, but it’s a nice casual read that will reassure you that the answer to the deeper parts of the question you are trying to ask is: No one knows.
Remember: there are no ignorant questions. There are only ignorant people. And on this topic, we are all ignorant, unless Cecil comes along and enlightens us. To date he has remained silent on exactly what the fabric of space is.
Yes, you can do this, but you don’t need to know anything except the acceleration force. Given a starting velocity, if you can measure your acceleration – which can be done as easily as you would measure gravitational acceleration on Earth – you can figure out your speed and position at any future point in time by simple integration. Of course, all you’re doing is tracking an imaginary speed and position, since in our scenario there’s no longer anything you can actually measure relative to.
Nope, can’t do this. From your point of view, the amount of energy required to accelerate in every direction is identical. Remember, you’re always traveling at precisely zero speed relative to yourself and your store of fuel, and that’s all that matters when it comes to hurling that fuel out the back (in some form or another) to change your momentum.
In order to keep track of what your speed and position “would be,” you need to at least know your initial velocity with respect to the old frame of reference.
Good, so it’s not just me then!
It’s hard to grasp, but you should realize that relativity is called by that name because every (inertial) reference frame is equivalent, so there’s no such thing as an absolute speed.
In your example, you can burn some fuel to accelerate by 0.1 c, but after you’ve accelerated, you’ll then again be at rest in your reference frame. You can do this a million times and still not notice anything funny going on, if there are not other objects out there to compare your speed to.
I guess you could have your flight engineer keep an accounting of the amount of fuel you’ve burned and your changing weight of the ship, to calculate what an outside observer would measure your speed to be relative to that old reference frame you were in, but so what? Now you’re in a different reference frame and yet again appear to be stationary w/ respect to yourself.
Or to put it another way: you can accellerate to 0.1c compared to anything but light. Compared to the speed of light as measured by you, you’re still standing still, no matter what your speed w/r/t anything else is.
You keep thinking in terms of Newtonian physics. Time and space aren’t constants in relativity!
To answer your first part of the question: Matter creates space and space creates time. Take away matter (the stars and planets), there would be no such thing as space or time.
The second part of your question is a bit trickier.
When you travel closer to the speed of light, the Universe contracts in the direction of travel, and time for you slows down. You wouldn’t see these effects because you’re stuck in your frame of reference.
Thus, if you shoot a beam of light out in front of your spaceship (which we’ll say is moving at 90% of the speed of light), you’ll see the light move at the speed of light in reference to your spaceship. In other words, you’ll see no difference no matter how fast or slow you’re traveling or which direction you shoot the beam of light. It will always move at the speed of light in reference to your spaceship.
The strange thing is that an outside observer would also see the beam move at the speed of light, but only a bit faster than your ship.
Here’s two thought experiments:
Your ship is moving at the speed of light, to you time is at a standstill. You look at your watch (well, you can’t because time is at a standstill, but let’s pretend). You see the time is 12:00.
You travel from Star “A” to Star “B” and look at your watch again, it still says 12:00 on it. How far apart are the two stars? By the way, the speed of light is 300 million meters per second. I’ll give you a few minutes to do the calculations. (You travel 300 millions meters per second for zero minutes. How far have you traveled?).
Okay, time’s up. Put down your paper and pencils. The correct answer is that the two stars are zero meters apart. When you move at the speed of light, the universe collapses into a flat pancake. Not only that, but if you look out the side window, you’ll notice that all events are taking place simultaneously in your two dimensional universe.
Experiment #2:
You are on a train box car with glass sides on your left and right. In the middle is a light source. The light source splits the beam and hits two detectors on the front and back of the train car. If you fire off a beam of light, you’ll notice that the light beam hits the front and back of your train car at the same time.
Let’s say, according to an outside observer, your train car is moving 50% of the speed of light. That observer sees you fire off a beam of light, and since the back of the train car is moving towards the beam and the front is moving away from the beam, that observer will see the beam of light hit the back of the train before the front of the train.
Now, according to the same observer, while he was watching this experiment, another train moving at 90% of the speed of light passes you on the far side.
What does an observer in this train see? He sees you moving in the opposite direction of the first observer. For the sake of simplicity, we’ll say he sees the train car as moving backwards. This new observer also sees the experiment. However, since the front of the car is moving towards the beam of light, and the back of the car is moving away from the beam of light, he sees the light strike the front of the car before the back of the car.
So, you all meet for lunch and discuss your findings:
You: The beam of light hit the back and front of the car at the same time.
First observer: No, the beam of light hit the back of the car before the front.
Second observer: Are you crazy? The beam of light clearly hit the front of the car before the back of the car!
Who’s right? All three observers are. The ordering of events, like time itself, is not fixed in relativity. It all depends upon the observer.
Mind blown? Then my work here is done.
Fascinating post, qazwart.
In your example of travelling at light speed you say that the distance between the stars A and B is zero meters and the time taken to travel is zero seconds. The thing I don’t understand is the concept of FTL travel, travelling at speeds faster then light. How could one travel between points faster than instantly?
Congratulations, you’ve just arrived at one of the classic proofs of the impossibility of FTL travel. Q.E.D.
Well, keep in mind that, while a ship traveling at light speed can travel between two stars 1000 light years apart instantaneously (from the travelers perspective), everyone else back home is dead because it’s been 1000 years (from everyone elses perpective). Plus, accelerating any mass to the speed of light requires infinite energy. So you can see that there are still a few downsides.
So your typical sci-fi FTL system uses some sort of (magical) teleportation or intra-dimensional hop to get around these limitations, so that time-dilation is either reduced or completely eliminated. Thus, one can make grand voyages across the stars without returning home to find that your great-great-great-great grandchild is pushing 92, and without having to use all the energy in the universe to do so.
Personally, I’m betting on felt. Some might favor corduroy, but I don’t think it’d have that kind of anisotropy.